Forest Fires and Mathematics

1. APEC-Tsukuba Conference 2014 Emergence Preparedness Education Forest Fires and Mathematics Moscow Center of Continuous Mathematical Education MCCME. Vysotskiy Ivan

2. Forest fires in Central Russia • The extreme heat of 2010 summer had caused the strongest fires in a number of regions of the Central and Volga Fede-ral districts. • The fires raged in 22 subjects of the Russia. • Happened about 30 000 of forest and peat fires on a total area of nearly1 mln ha. The map of the fires and smokes over Central Russia, 2010 (photo by NASA) MCCME. Vysotskiy Ivan

3. Forest fires in Central Russia • Burned about 2 5000 of living buildings. • The fire got to nuclear centers located in Sarov (Nizhniy Novgorod region) and Snezhinsk (Chelyabinsk region). • In connection with the fire situation in 7 regions – N.Novgorod, Voronezh, Vladimir, Moscow and Ryazan regions, Mari El and Mordovia the emergency regime has been introduced. MCCME. Vysotskiy Ivan

4. Forest fires in Central Russia • In the 1990s the Russian state and government couldn't support forestry and fire-prevention measures on boundless spaces of Russian forests. As the result: • Overgrowing of fire-breaks • Reducing the forestries and foresters in number and funding • The fire aviation had declined • All these factors have led to increased losses from forest fires that had been uncontrolledly spreading over vast territories, closely approaching the towns and villages. MCCME. Vysotskiy Ivan

5. Burning peatbogs • The main danger for the major cities is the toxic smoke from burning peat in the suburb area. • Peat is able for combustion if the humidity is less than 40 %. • The depth of burning might be limited to the level of groundwater. Peat fire can last months and years. Peat burns in summer and in winter it burns too MCCME. Vysotskiy Ivan

6. Moscow Smoky August (2010) • In July and August 2010 smoke from peatlands covered Moscow. • Fragments of the chronicle (http://ru.wikipedia.org). • Aug 6. Halted the work of the German Embassy in Moscow • Aug 7. Disrupted the work of Moscow airports. • Aug 8. Stopped shipping in the Moscow river • Aug9 . The Head of the Moscow Health Department had stated that due to the smoke the mortality in Moscow has doubled. Walking in Moscow Aug 2010. The Kremlin MCCME. Vysotskiy Ivan

7. Moscow Smoky August (2010) The root cause of natural peat fires, and because of which formed smoke, was active drainage of wetlands and extracting peat in 20-60 years of the XX century under the project of electrification (GOELRO). Arpt. Sheremet’evo. Aug 2010. By S.Gutnikov In the late 60-ies due to the active development oil and gas industry need in peat decreased. Drained peatbogs began to be closed, but were not filled with water. MCCME. Vysotskiy Ivan

8. What has school math to do with it? Four aspects Forecasting Modeling Behavior Liquidation of consequences MCCME. Vysotskiy Ivan

9. Forecasting and forecasts • Predictions are very interesting but are outside the scope of science. • Forecasting natural disasters is a daunting challenge, which does not yet have a satisfactory solution. • We offer not to create a false ideas of what our students can learn about forecasting natural disasters within lessons of mathematics. It concerns not only students but teachers first of all. MCCME. Vysotskiy Ivan

10. Modeling MCCME. Vysotskiy Ivan

11. Modeling • Any serious and credible modeling of complex natural phenomena (such as forest fires or floods) can not be reached by means of school mathematics or physics. Conclusion: Here we are bound to attract attention of the Governments and Public to the fact that mathematics today makes technology of the future. If we want to understand better nature in 20-30 years, now we have to support math education as the base for long-term development. MCCME. Vysotskiy Ivan

12. Behavior • The value of disaster preparedness education can hardly be overestimated. • There is only one doubt – is this really topic for lessons of mathematics? • Much more important are the lessons of life safety, in which students are taught to understand the nature of disasters specific to the region and to act correctly when this disaster happened. MCCME. Vysotskiy Ivan

13. Liquidation of consequences Liquidation of a disaster consequences is mainly a question of funding. The question of insurance of property and home arises for discussion and regrets in our country every time immediately after large-scale natural disasters. MCCME. Vysotskiy Ivan

14. Insurance • In 2010 this was caused with wildfires. Most of the payments received from the federal budget . • In 2013 the reason was a flood in the Far East, when it became clear that the main burden of compensation again falls on the budget because only 10 percent of the population had insured their own apartments and houses . • State compensation never covers all losses (can’t). • Centralized mechanism of financial compensation works slowly and formally, becomes asubject to fraudulent schemes, plain theft and corruption. MCCME. Vysotskiy Ivan

15. Lack of insurance literacy In countries with developed market economies, it is generally accepted that the insurance industry is a strategic sector of the economy. However, in Russia the insurance business has not become a part of the public culture so far. Most people have lack an understanding of the spirit and purpose of the insurance. Therefore, citizens and public servants and even employees of insurance companies need to learn more about insurance principles. MCCME. Vysotskiy Ivan

16. This is our business Therefore, the increase in literacy in matters of insurance is a priority if we are talking about the elimination of consequences of natural disasters. Here math lessons in school can help greatly The post mark “225 years since the first insurance company has been established n Russia” Post of Russia, 2011 MCCME. Vysotskiy Ivan

17. The Conception of math education development On December 24 of 2013 Russian Government had accepted The Conception of Mathematical Education Development in accordance with the charge of Russian President given in May of 2012. It is rather short document that sets the main goals and principles of math education in schools and universities. Firstly in latest history the Russian Government states unsatisfactory status of common and compulsory math education and announces the necessity to implement the education on different levels depending on individual educational interests and demands of a student. MCCME. Vysotskiy Ivan

18. Three levels • The First Level – for life • The Second Level – for professional activity • The Third Level – for mathematical creativity and fundamental science development Regarding the First Level the Conception underlines that every student must reach mathematical literacy enough for everyday life. This include elementary statistical and probabilistic literacy which are expected as a part of common public culture. MCCME. Vysotskiy Ivan

19. Statistics and probability in Russian schools • Since 2004 statistics and elements of probabilities theory are included in Federal Educational Standards. • Now we have got the first successful experience in teaching statistics and preparing teachers for this. • Banking, management, insurance and other public phenomena bear probabilistic character and we pay much attention on these subjects in our curriculum when planning the course of statistics and probability for middle and high school. MCCME. Vysotskiy Ivan

20. Regular textbooks • In 2004 our group leaded by Prof. Y.Tjurin had issued the first regular textbook for 7-9 grades on Probabilities and Statistics for Moscow. Now it is in use not only in Moscow. • In 2014 we finished and issued the textbook for 10-11 as a sequel of the first one MCCME. Vysotskiy Ivan

21. Insurance literacy is a part of probability for 7-11 grades As the way from school mathematics to everyday events lies through learning statistics, we can apply various subjects to design the lessons and poses the problems. So we do when talking about life safety and natural disasters in teaching and studying statistics. The first example has been dragged out from the lesson in grade 7 MCCME. Vysotskiy Ivan

22. The lesson for 7 – 8 grade. Comparison and hypotheses • The main task is to involve students into discussion about some features of two kindred charts. • The teacher tries to wake the ability for comparison and putting hypotheses. • Being out of possibility to check set hypotheses we shouldn’t encourage students to think they and prove but we want them to fantasize and seek and put convincing arguments and reasons. MCCME. Vysotskiy Ivan

23. Two charts The left one shows number of payments, the right shows the total paid within two risks (buildings and property lost in fires including wildfires) MCCME. Vysotskiy Ivan

24. Two charts 4. What can you propose to explain why in 2007 the number of payments was much less then in other years? Your hypotheses, please… 5. How should you explain why in 2006 the number of payments is less while the total amount is greater than in other years? Hypotheses, please… 6. How might it be that total insurance compensation for lost property is growing year by year when the number of payments is oscillating? 7. What could you assume about quantity of insurants and the tendency? 3. What significantly influences the total amount of payments? 1. What specialties you can notice in the charts? 2. What significantly influences the number of payments? 8. Can you make any assumption about the strategy ofthe insurance companies? MCCME. Vysotskiy Ivan

25. The conclusion • The lesson had been designed to encourage students to hypothesize and make assumptions from graphically presented information. It’s no important that we have no enough data to check the hypotheses. The best tool of a statistician is his culture, intuition and fantasy with which he processes the statistical data. • The second aim is increasing understanding about insurance as a way to defend homes and property when a disaster occurs. So the teacher must focus on the tendency of growing the number of insurants and insured sum through the years. MCCME. Vysotskiy Ivan

26. 9 – 11 grades. Math Expectation of a Discreet Random Value One of the main our ideas is to lead students to the understanding effect of Large Numbers Law. So the concept of ME grows to one of the central concepts. We try to explain to teachers that the very core of ME is very simple – ME plays the role of “theoretical average”. We success slowly. The lesson below is designed as a mathematical play with the subject concerning the insurance business as the business of very probabilistic nature. MCCME. Vysotskiy Ivan

27. How to manage an insurance company? We want to establish an insurance company in a rural area of Central Russia. Our specialization might be the insurance of living buildings and property against wildfires. Now we offer only one kind of insures risk: “Loss or damage of wood buildings and property in a fire” MCCME. Vysotskiy Ivan

28. What is the insurance premium? • Determine for ourselves that an insurance company is not a charitable corporation. It exists and works due to insurance premiums paid by insurants. The company mustn’t work for losses. • Now we will consider only mathematical aspect of forming premiums. MCCME. Vysotskiy Ivan

29. What makes the insurance premium? Now please put assumptions – what the premium depends on? Which items are more sufficient, which – less? The total sum of assumed insurance compensation 2. The probability of the insurance accident 3. Common weal Number of insurants 5. Competition on insurance market 6. Governmental regulation of insurance activity 7. The necessity income of the company (including necessary for salary, rent, taxes, covering accidents etc.) MCCME. Vysotskiy Ivan

30. Main factors The teacher must lead students to the main ideas that most sufficient factors are: • The total sum of assumed insurance compensation • The probability of the insurance accident • 3. The necessity income of the company (including necessary for salary, rent, taxes, covering accidents etc.) We can discuss all of them but all rest are additional factors we have to take into account. Lets return to them later MCCME. Vysotskiy Ivan

31. Assumptions and followings Lets accept that for successful operating our company must get the average 200 rub from one insurance policy (one insurant). Let Xis the insurance compensa-tion in an accident for one policy. The premium equals A rub. To get not less than 200 rub in average we need provide the inequality Where EXis the math expectation of the compensation to be paid in an accident. MCCME. Vysotskiy Ivan

32. Values and probabilities So we must learn about values of X and their probabilities. After studying many factors in the region (which are the main?) we define our base compensations: MCCME. Vysotskiy Ivan

33. Values and probabilities • What do we need more? Probabilities. • What do you think of which risk is greater – of the full destruction or partial loss or an insufficient damage? • What do we have to do to know about them?Collect the data of observation for some years to find the frequency for every of accident type as an estimators for the probabilities. Let’s assume that after the serious research we learnt three probabilities MCCME. Vysotskiy Ivan

34. The comment • We have posed much simplified problem. What didn’t we take into account? • The compensations might be more various. • Insurants are in various conditions and the fire is not equally probable for all of them. • Can we take into account absolutely all circumstances for all insurants? • Insurance gives the averaging probable risks • and compensations MCCME. Vysotskiy Ivan

35. The fourth probability When making the table which case did we forget? We see that the probability of luck issue is greatest and close to 1. This is a main principle of insurance. MCCME. Vysotskiy Ivan

36. The distributionand ME Now we’ve got the distribution of X: Find the expectation: So MCCME. Vysotskiy Ivan

37. Why does it work? If we assume the policy price (premium) to be exactly 2000 rub and all our assumption are true then we’ll get the minimal necessary income. This is provided by Large Numbers Law, which says that the true average compensation must be close to the found math expectation if we sell enough of policies (have enough of customers). MCCME. Vysotskiy Ivan

38. The questions • What if we highlyincrease the price for the policy? • What might happen if we sell not very many of policies? • What would change if the number of insurants grows and we sell much more policies than now? • What would happen if we got wrong in estimating probabilities? • What if a huge fire occurs and the quantity of injured people grows much more than we could forecast? • What can we do to make our model more complicated and flexible? MCCME. Vysotskiy Ivan

39. The homework • Suggest to make the model and solve the problem about the minimal premium with another assumptions. Moreover – give the questions set above to think about. On the next lesson the posed questions must be discussed. • Firstly one can decide it is not math. The one is wrong. Such “non-mathematical” discussions develop students abilities for creative and critical thinking, making conclusions and hypotheses better than solving problems in traditional school math. MCCME. Vysotskiy Ivan

40. More • The presented lessons make only small part of possible examples how to connect nature and school math using probability. • Try to design a lesson dedicated to probabilistic estimation of reserves (water, food, medicines)needed for shelters in a city. We can proceed from given population, known probability that a dweller comes to the shelter, from known average duration of stay. • What would change if we make two small shelters in different districts of the city instead of one large? Assure you – this is good and not simple problems to discuss and solve mathematically. How to do it in most interesting way? MCCME. Vysotskiy Ivan

41. Thanks for your attention MCCME. Vysotskiy Ivan